Lesson: Pascal’s Triangle and the Binomial Theorem Mathematics

In this lesson, we will learn how to use Pascal’s triangle to find the coefficients of the algebraic expansion of any binomial expression of the form (𝑎+𝑏)ⁿ.

Lesson Plan

Students will be able to

expand a binomial expression of the form using Pascal’s triangle to find the coefficients of the terms.

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Worksheet

Q1:

Michael has been exploring the relationship between Pascal’s triangle and the binomial expansion. He has noticed that each row of Pascal’s triangle can be used to determine the coefficients of the binomial expansion of , as shown in the figure. For example, the fifth row of Pascal’s triangle can be used to determine the coefficients of the expansion of .

By calculating the next row of Pascal’s triangle, find the coefficients of the expansion of .

Michael now wants to calculate the coefficients for each of the terms of the expansion . By substituting into the expression above, or otherwise, calculate all of the coefficients of the expansion.

Q2:

Matthew knows that he can use the row of Pascal’s triangle to calculate the coefficients of the expansion .

Calculate the numbers in the row of Pascal’s triangle and, hence, write out the coefficients of the expansion .

Now, by considering the different powers of and and using Pascal’s triangle, work out the coefficients of the expansion .

Q3:

Shown is a partially filled-in picture of Pascal’s triangle. By spotting patterns, or otherwise, find the values of , , , and .